Triangulation of Microstructure using Recursive Subdivision
and Advancing Front Technique

Daniel Rypl, Zdeněk Bittnar

Department of Mechanics
Faculty of Civil Engineering
Czech Technical University in Prague
Thákurova 7, 166 29 Prague, Czech Republic



Abstract:

The present paper deals with the discretization of microstructure initially described by a voxel based representation yielding a triangulation of variable resolution. Firstly, the gray scale digital representation is thresholded into voxels of appropriate discrete values of gray corresponding to individual phases of the processed microstructure. In the next phase, the boundary voxels (and their boundary sides) of individual phases are identified. A triangulated boundary representation (of the same resolution as the initial voxel representation) is then obtained from the boundary voxel representation by replacing the boundary sides of boundary voxels by semi-regular triangulation with nodes at the centres of those boundary sides. In this triangulated boundary representation, the individual surfaces (and their boundary curves) bounding individual phases of the microstructure are identified and then subjected to recursive interpolating subdivision yielding a C1 continuous surface. In the final phase, the individual smooth boundary surfaces are triangulated using the Advancing Front Technique. Since there is available no global mapping of the recovered surfaces, the discretization is performed directly in 3D space on the surface. Note that the resolution of the final triangulation is independent of the resolution of the initial digital representations and is driven mainly by the user specification and properties (curvature) of the recovered smooth representation. The performance of the proposed approach is shown on an example.